Question

Which expression models the length, from point A to point O, of the portion of the number line that is shown?
Responses
A −7 + (−7)−7 + (−7)
B −7 + 7−7 + 7
C |−7 − 7||−7 − 7|
D |−7 − (−7)|

Answer 1

To determine the correct expression that models the length from point A to point O on the number line, we should interpret the points and their positions carefully.

Typically, if A is at \(-7\) and if point O is at \(0\), the length from point A to point O can be found using the absolute value:

\[
|A - O| = |-7 - 0| = | -7 | = 7
\]

However, let's analyze the answer choices provided:

A) \(−7 + (−7)−7 + (−7)\)

B) \(−7 + 7−7 + 7\)

C) \(|−7 − 7||−7 − 7|\)

D) \(|−7 − (−7)|\)

Among these choices, we are looking for an expression that calculates the distance from point A (-7) to point O (0).

**Choice D**: \(|−7 − (−7)|\) simplifies to:

\[
|−7 + 7| = |0| = 0
\]

This does not represent the length from point A to point O.

Now let's evaluate the other options:

**Choice C**: \(|−7 − 7||−7 − 7|\) simplifies to:

\[
|−14||−14| = 14 \cdot 14 = 196
\]

Clearly, this does not represent the distance from -7 to 0.

**Choice B**: \(-7 + 7−7 + 7\) simplifies to:

\[
0 - 7 + 7 = 0
\]

Again, not the intended length.

**Choice A**: \(-7 + (−7)−7 + (−7)\) evaluates to:

\[
-7 - 7 - 7 - 7 = -28
\]

Although each of these choices does not directly compute the expected distance from -7 to 0, **none represent the distance** logically.

Out of these choices, if you purely want to model the distance, **there is no choice that represents the correct calculation.** The best model in common context to express distance would be \(|−7| = 7\) if that was an available option.

Thus, if you are strictly sticking to the options given, I would suggest D based on it being the least incorrect, but make note that this is indeed not the precise model you’re seeking for length.

The final answer is **none of the expressions correctly model the length from point A (-7) to point O (0).**